Ever hear of Kirchoff's Voltage Rule? Looks like this:
E = ( I X R) + Ke
It means the supply voltage is equal to the current times the resistance plus the BEMF voltage.
16 Volts = ( 20 amps x .4000 Ohms Terminal ) + Ke
16 - ( 8.0 ) = Ke 8 volts BEMF
Lets say the motor spins 60,000 RPM. Half = 30,000 and at this speed puts up 8 volts of back
EMF such as this law states. What are the millivolts per 1,000 RPM according to the motor constant
30,000 / 1,000 = 30 then 8 / 30 = .2666**** Millivolts per amp.
(.2666 millivolts / 104.7197) * .73756 = .0018776 pounds feet per amp.
.0018776 * 20 amps = .037552 pounds feet.
(30,000 rpm * .037562) / 5252 = .2145 horsepower
.2145 * 745.7 = 160 watts out put.
Input = ((16 / .400 ) * 16 ) / 2 = 320 watts
160 / 320 = 50 % Efficiency and thats as good as it gets for that resistance, at that voltage and at
that RPM. (No friction has been taken from the Gross)
I used this voltage and terminal resistance because the math was easy and even.
Kirchoff's rule is satisfied as is the motor constant rule that says:
Ke = Kt = 1/Kv
(Numbers above in green are conversion constants)
Lets change the speed to 50,000 RPM. We added some magnet.
25,000 / 1,000 = 25 then 8 / 25 = .3200 millivolts per thousand
(.32 / 104.7197 ) * .73756 = .0022537
.0022537 * 20 = .045074
( 25,000 * .045074 ) / 5252 = 2145563 * 745.7 = 160 watts output = 160 / 320 = 50% efficiency.
Now look at the picture at the top of this page and you see the Program with these parameters
plugged into it with the exact same results PLUS the guide line numbers I think are important. Well to
Note these boxes: Torque efficiency and Voltage Unity. Both 100%. These are your flux guide line
boxes. Mismatches between magnet and armature or silly timing numbers mess these up. That means
that 1/Kv and Ke are not equal.
You already know that when you half the speed the torque is doubled thus the horsepower
remains the same as does efficiency. That tells you something very important. For any given armature
there are only three areas of concern:
1.) Friction and windage which is basically nil anyway if the motor is close to right.
2.) Commutation. Getting the resistance as low as possible at the terminals is HUGE.
3.) IF those boxes for unity are not at 100% you have work to do in the area of flux management.
For any given resistance at the terminal the maximum amount of power is laid in stone. For .400
ohms of resistance at 16 volts there is nothing you can do to get past 160 watts at the pinion except
increase track voltage.
This is a rock solid tool that has the dyno packed in a box. Three measurement tell me everything
I can possibly know about my motor when laid into this program. It cuts through the crap and gets past
the egos of the "experts".
Now I will make it easier yet.
Measure the terminal resistance via the Kelvin four wire method and a decent meter. Spin the
motor up to 4 volts or so and take the rpm measurement. With these two pieces of information you can
calculate the generator constant. Do that. Now measure it and if it doesn't match get to work.
This little Parma arm motor I've been working on to develop this tool started with a unity number
of 83.77% and a terminal resistance of .5002 Ohms. Made 115 watts.
A bit of work to the flux field and it has improved to a unity number of 97.27% and a terminal
resistance of .4361 Ohms for 138 watts net. Not bad for a green arm. That little miss off the 100% mark
is the frictional losses. Back those out and old girl is hugging Unity. The only way to wring more power
out of it is the lower the terminal resistance if at all possible and I'm not sure it is. This is about 12
watts more power than I have ever got out of one of these armatures.